A great deal of effort has been directed to analyzing networks in which flows of various types (e.g., fluids, electricity or representational quantities) move from node to node through conduits having specified capacities. For example, it is well known that it often is desirable to identify the “minimum cut” of, and/or the “maximum flow” through, such a network. However, obtaining such information often is very time-consuming and computationally expensive, particularly when analyzing very large networks, and particularly when the conduit capacities are not fixed but rather depend upon a specified parameter and one wishes to identify the entire set of minimum cuts and/or maximum flows across all (or at least a range of) values for the parameter.